Problem: Given $ m \angle MON = 3x + 55$, $ m \angle LOM = 5x + 83$, and $ m \angle LON = 154$, find $m\angle LOM$. $O$ $L$ $N$ $M$
From the diagram, we see that together ${\angle LOM}$ and ${\angle MON}$ form ${\angle LON}$ , so $ {m\angle LOM} + {m\angle MON} = {m\angle LON}$ Substitute in the expressions that were given for each measure: $ {5x + 83} + {3x + 55} = {154}$ Combine like terms: $ 8x + 138 = 154$ Subtract $138$ from both sides: $ 8x = 16$ Divide both sides by $8$ to find $x$ $ x = 2$ Substitute $2$ for $x$ in the expression that was given for $m\angle LOM$ $ m\angle LOM = 5({2}) + 83$ Simplify: $ {m\angle LOM = 10 + 83}$ So ${m\angle LOM = 93}$.